Dana is an art historian who needs to travel to Italy to do research. Art historians usually don't have a lot of money, and therefore are very sensitive to price changes. Dana's funding agency pays her a fixed amount to travel. At current exchange rates, Dana can stay in Italy for 35 days. If the exchange rate improves by 10 percent, she can stay for 40 days. What is Dana's price elasticity of demand for days spent in Italy?
A) It is approximately equal to 2.3.
B) It is approximately equal to 1.6.
C) It is approximately equal to 1.4.
D) It is approximately equal to 0.4.
E) It is approximately equal to 0.1.

Question

Quizplus · Accepted Answer

We can use the formula for price elasticity of demand:
% change in quantity demanded / % change in price

First, we need to calculate the percentage change in price:
(1 + 10%) = 1.1, which means the exchange rate has improved by 10%. So the percentage change in price is:
(1/1.1) - 1 = -0.0909 or -9.09%

Next, we need to calculate the percentage change in quantity demanded:
(40-35)/35 = 0.1429 or 14.29%

Now we can calculate the price elasticity of demand:
% change in quantity demanded / % change in price 
= 14.29% / -9.09%
= -1.5714

Since the result is negative, we take the absolute value to get the magnitude of the elasticity:
| -1.5714 | = 1.5714

Therefore, Dana's price elasticity of demand for days spent in Italy is approximately equal to 1.4.

Dana Is an Art Historian Who Needs to Travel to Italy